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Topic models Source: Topic models, David Blei, MLSS 09

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Topic modeling - Motivation

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Discover topics from a corpus

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Model connections between topics

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Model the evolution of topics over time

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Image annotation

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Extensions* Malleable: Can be quickly extended for data with tags (side information), class label, etc The (approximate) inference methods can be readily translated in many cases Most datasets can be converted to bag-of- words format using a codebook representation and LDA style models can be readily applied (can work with continuous observations too) *YMMV

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Connection to ML research

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Latent Dirichlet Allocation

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LDA

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Probabilistic modeling

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Intuition behind LDA

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Generative model

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The posterior distribution

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Graphical models (Aside)

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LDA model

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Dirichlet distribution

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Dirichlet Examples Darker implies lower magnitude \alpha < 1 leads to sparser topics

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LDA

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Inference in LDA

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Example inference

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Topics vs words

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Explore and browse document collections

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Why does LDA work ?

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LDA is modular, general, useful

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Approximate inference An excellent reference is On smoothing and inference for topic models Asuncion et al. (2009).

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Posterior distribution for LDA The only parameters we need to estimate are \alpha, \beta

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Posterior distribution

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Posterior distribution for LDA Can integrate out either \theta or z, but not both Marginalize \theta => z ~ Polya (\alpha) Polya distribution also known as Dirichlet compound multinomial (models burstiness) Most algorithms marginalize out \theta

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MAP inference Integrate out z Treat \theta as random variable Can use EM algorithm Updates very similar to that of PLSA (except for additional regularization terms)

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Collapsed Gibbs sampling

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Variational inference Can think of this as extension of EM where we compute expectations w.r.t variational distribution instead of true posterior

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Mean field variational inference

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MFVI and conditional exponential families

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Variational inference

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Variational inference for LDA

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Collapsed variational inference MFVI: \theta, z assumed to be independent \theta can be marginalized out exactly Variational inference algorithm operating on the collapsed space as CGS Strictly better lower bound than VB Can think of soft CGS where we propagate uncertainty by using probabilities than samples

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Estimating the topics

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Inference comparison

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Comparison of updates On smoothing and inference for topic models Asuncion et al. (2009). MAP VB CVB0 CGS

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Choice of inference algorithm Depends on vocabulary size (V), number of words per document (say N_i) Collapsed algorithms – Not parallelizable CGS - need to draw multiple samples of topic assignments for multiple occurrences of same word (slow when N_i >> V) MAP – Fast, but performs poor when N_i << V CVB0 - Good tradeoff between computational complexity and perplexity

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Supervised and relational topic models

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Supervised LDA

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Variational inference in sLDA

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ML estimation

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Prediction

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Example: Movie reviews

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Diverse response types with GLMs

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Example: Multi class classification

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Supervised topic models

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Upstream vs downstream models Upstream: Conditional models Downstream: The predictor variable is generated based on actually observed z than \theta which is E(zs)

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Relational topic models

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Predictive performance of one type given the other

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Predicting links from documents

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Things we didnt address Model selection: Non parametric Bayesian approaches Hyperparameter tuning Evaluation can be a bit tricky (comparing approximate bounds) for LDA, but can use traditional metrics in supervised versions

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Thank you!

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